R programming competition : A clinic has three doctors. Patients come into the clinic at random, starting at 9 a.m. The time after opening at which the first patient appears follows an exponential distribution with expectation of 10 minutes and then, after each patient arrives, the waiting time until the next patient is independently exponentially distributed, also with expectation of 10 minutes. When a patient arrives, he or she waits until a doctor is available. The amount of time spent by each doctor with each patient is a random variable, uniformly distributed between 5 and 20 minutes. The office stops admitting new patients at 4 p.m. and closes when the last patient is through with the doctor. [35 points] (a) Simulate this process once. (i) How many patients came to the office? (ii) How many had to wait for a doctor? (iii) What was their average wait? (iv) When did the office close? (b) Simulate the process 1000 times and estimate the median for each of the summaries in (a).